Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,6,22}

Atlas Canonical Name {2,6,22}*528

Overview

Group
SmallGroup(528,164)
Rank
4
Schläfli Type
{2,6,22}
Vertices, edges, …
2, 6, 66, 22
Order of s0s1s2s3
66
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

6-fold

11-fold

22-fold

33-fold

Covers minimal covers in bold

2-fold

3-fold

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (14,25)(15,26)(16,27)(17,28)(18,29)(19,30)(20,31)(21,32)(22,33)(23,34)(24,35)(47,58)(48,59)(49,60)(50,61)(51,62)(52,63)(53,64)(54,65)(55,66)(56,67)(57,68);;
s2 := ( 3,14)( 4,24)( 5,23)( 6,22)( 7,21)( 8,20)( 9,19)(10,18)(11,17)(12,16)(13,15)(26,35)(27,34)(28,33)(29,32)(30,31)(36,47)(37,57)(38,56)(39,55)(40,54)(41,53)(42,52)(43,51)(44,50)(45,49)(46,48)(59,68)(60,67)(61,66)(62,65)(63,64);;
s3 := ( 3,37)( 4,36)( 5,46)( 6,45)( 7,44)( 8,43)( 9,42)(10,41)(11,40)(12,39)(13,38)(14,48)(15,47)(16,57)(17,56)(18,55)(19,54)(20,53)(21,52)(22,51)(23,50)(24,49)(25,59)(26,58)(27,68)(28,67)(29,66)(30,65)(31,64)(32,63)(33,62)(34,61)(35,60);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(68)!(1,2);
s1 := Sym(68)!(14,25)(15,26)(16,27)(17,28)(18,29)(19,30)(20,31)(21,32)(22,33)(23,34)(24,35)(47,58)(48,59)(49,60)(50,61)(51,62)(52,63)(53,64)(54,65)(55,66)(56,67)(57,68);
s2 := Sym(68)!( 3,14)( 4,24)( 5,23)( 6,22)( 7,21)( 8,20)( 9,19)(10,18)(11,17)(12,16)(13,15)(26,35)(27,34)(28,33)(29,32)(30,31)(36,47)(37,57)(38,56)(39,55)(40,54)(41,53)(42,52)(43,51)(44,50)(45,49)(46,48)(59,68)(60,67)(61,66)(62,65)(63,64);
s3 := Sym(68)!( 3,37)( 4,36)( 5,46)( 6,45)( 7,44)( 8,43)( 9,42)(10,41)(11,40)(12,39)(13,38)(14,48)(15,47)(16,57)(17,56)(18,55)(19,54)(20,53)(21,52)(22,51)(23,50)(24,49)(25,59)(26,58)(27,68)(28,67)(29,66)(30,65)(31,64)(32,63)(33,62)(34,61)(35,60);
poly := sub<Sym(68)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;